Lakes have connected rivers and streams that provide paths for fish and eggs to move around. There are human and animal activities that affect this. Your bird example and beavers causing floods could allow movement.
So many lakes do not have rivers flowing in and out. A low spot in an area will become a lake.
Many do have rivers; many don't. Ponds even more so don't have attached rivers.
Isolated alpine lakes do not have connected rivers and streams, yet a ton are stocked with fish by humans.
Is it unbelievable that ancient hunter-gatherers would do the same thing?